Wagner Theory Research Articles

Long-term aging behavior and mechanism of CMSX-4 nickel-based single crystal superalloy at 950 ℃ and 1050 ℃

Nickel-based single crystal superalloys CMSX-4 have been widely used to manufacture aeroengine turbine blades because of their excellent high-temperature comprehensive properties. The microstructure evolution behavior, mechanism, and influence on micromechanical behavior of the second-generation nickel-based single crystal superalloy during long-term aging at 950°C and 1050°C for 10–2000 h were investigated. The results show that, with the extension of aging time, the average size of γ' phase increased, whose morphology changed from square block to strip and L shape and rafting phenomenon was observed. The coarsening of γ' conforms to Lifshitz–Slyozov–Wagner (LSW) theory and the coarsening rates are 4.241×10−5 and 9.954×10−5μm3/h at 950°C and 1050°C, respectively. After aging at 950°C and 1050°C for 1000 h, segregation of refractory elements was formed in the samples. There are hard topological close-packed (TCP) phases surrounded by γ' envelope precipitates, which destroyed the continuous structure of γ'. The precipitation of TCP caused the depletion of refractory element Re in the γ' envelope phases, resulting in softening effect. It was also found that high temperature can not only accelerate the coarsening of γ' phase but also promote the precipitation and growth of TCP phases.

Droplet impact onto a porous substrate: a Wagner theory for early-stage spreading

An analytical model for droplet impact onto a porous substrate is presented, based on Wagner theory. An idealised substrate boundary condition is introduced, mimicking the effect of fluid entry into a genuinely porous substrate. The asymptotic analysis yields a solution for a small porous correction with free-surfaces and pressures compared with the impermeable case. On a global scale, it is found that the impact region on the substrate grows more slowly with porosity included due to loss of mass into the substrate. The spatial distribution of liquid volume flux into the substrate is also described. Locally near the turn-over regions, the expected jetting along the surface is calculated with the same volume flux but the jet is found to be slower and thicker than for an impermeable substrate.

Water entry of an elastic conical shell

The axisymmetric problem of a conical shell impact onto an inviscid and incompressible liquid of infinite depth is studied. The shell is thin, and its deadrise angle is small. The problem is inertia dominated. Gravity, surface tension and viscous effects are not taken into account. The hydrodynamic loads acting on the shell and the shell displacements are determined at the same time. The model by Scolan (J. Sound Vib., vol. 277, issue 1–2, 2004, pp. 163–203) is used to find the flow and hydrodynamic pressure caused by the shell impact. This model is based on the Wagner theory of water impact, which was generalised to axisymmetric problems of hydroelastic slamming. Dry and wet modes of the conical shell, as well as the corresponding frequencies, are calculated. It is shown that a conical shell can be approximated by a circular plate only for a very small deadrise angle. Deflections and strains in the conical shell during the impact stage, when the wetted part of the shell increases at high rate, as well as the hydrodynamic loads, are determined and analysed.

Effect of calcination temperature on structural, magnetic, and dielectric properties of Mg0.75Zn0.25Al0.2Fe1.8O4 ferrites

Based on the desire to improve material properties, the effects of temperature have begun to be investigated. It was found that for nano-sized powder materials, such as ferrites, the structural properties like crystal structure and grain size, as well as many magnetic and electrical properties depending on them, change with the calcination temperature. Considering these changes, the effect of calcination temperature on the structural, magnetic, and electrical properties of MZA ferrites (Mg0.75Zn0.25Al0.2Fe1.8O4) prepared by co-precipitation was investigated in this study. The produced MZA ferrites were calcined at three different temperatures (600, 700, and 800 °C). The X-ray diffraction results showed that the samples exhibited a cubic spinel structure. It was found that the crystal sizes (D_sch) calculated using the Debye-Scherrer equation increased with increasing calcination temperature (22.47, 33.53, and 42.53 nm). From the Williamson–Hall (W–H) plots, crystal sizes were calculated almost same as Debye–Scherrer crystal sizes. The nano-sized particles were examined by scanning electron microscope (SEM). Elemental analysis was performed using EDX. ν1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ u }_{1}$$\\end{document} and ν2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ u }_{2}$$\\end{document} absorption bands and O–H and C–H vibrations were detected in the FTIR spectra. Magnetic measurements were carried out at room temperature and in the range of ± 60 kOe under the applied field. Magnetic results are explained by superparamagnetism. Dielectric measurements were performed at room temperature and a frequency range of 20 Hz to 10 MHz. The dielectric properties can be explained by Maxwell–Wagner theory. Impedance spectroscopy study revealed that the relaxation mechanism is consistent with the Cole–Cole model. In AC conductivity studies at room temperature, it was found that the sample calcined at 600 °C would be suitable for energy storage devices.

The effect of a nonlinear energy sink on the gust response of a wing

In this paper, the potential effectiveness of a nonlinear energy sink (NES) to absorb the energy from a wing that is vibrating as a result of flying in a gusty environment is investigated. The structural dynamics of the wing is simulated using a rigid airfoil mounted on two linear/nonlinear springs to represent the bending and torsional stiffness of the wing. The wing is subjected to a combination of gust and aerodynamic loads. The unsteady aerodynamic lift and moment are modelled using Wagner's theory. Furthermore, the gust loads are obtained by assuming two different gust profiles, e.g. sharp-edged and 1-cosine gust profiles. A nonlinear energy sink, which comprises of a concentrated mass, damper and a nonlinear spring, is attached to the wing, and its effectiveness to absorb the gust energy is investigated. The coupled nonlinear aeroelastic equations are integrated numerically to determine the response of the wing. To verify the developed aeroelastic model, the obtained results are compared with the available results in the literature and an excellent agreement is observed. The results highlight that adding the NES to the wing is capable of reducing the gust oscillation amplitude of the wing significantly when the NES parameters are chosen accordingly.

Investigation of fluid added mass matrix during hydroelastic slamming of wedges

The investigation of the fluid added mass (FAM) matrix during the water entry of an elastic structure is crucial for understanding the mechanism of hydroelastic slamming, as it characterizes the fluid–structural interaction process. In this paper, we excavate a model for directly estimating the FAM matrix during hydroelastic slamming and employ this model to study the limitations and optimized values of the relaxation factor for a partitioned coupling solver. Our simulation of hydroelastic slamming couples the Wagner theory with the modal superposition method (MSM), and the FAM matrix is computed using a monolithic coupling scheme. We conduct a series of parametric studies to analyze how the modal number, hydroelasticity, deadrise angle, and structural boundary condition influence the eigenvalues of the FAM matrix. Based on these studies, we then propose an analytical model to directly express the eigenvalues of the FAM matrix, demonstrating their linear relationship with the wetted ratio. Furthermore, we apply this analytical model to analyze the relaxation factor in the partitioned coupling scheme, theoretically explaining its strong connection to the FAM effect. The limitations and optimized values of the relaxation factor are theoretically presented, and these results are verified through our numerical tests.

Phase transformation kinetics in a homogenised cast alloy 625 and its impact on deformation micromechanisms

ABSTRACT This study focuses on understanding the impact of sequential ageing on the microstructural evolution of a large-grained structure homogenised cast alloy 625 and its effect on mechanical properties. SEM and TEM analyses of aged samples were conducted to comprehend various precipitation micromechanisms such as (i) nucleation and growth kinetics of γ′′ phase and (ii) transformation of primary carbides and grain boundary phase(s) evolved. The MC-based primary carbides are ascertained to transform into M23C6 secondary carbides following two completely different pathways: (I) MC + γ→ M23C6 + δ (mainly at grain boundary) and (II) MC + γ→M23C6 + γ″ (mainly within matrix). Furthermore, all three variants of γ″ phase are detected to evolve in the matrix displaying a crystallographic orientation of [001]γ″ // < 001>γ, and {100}γ″ // {100}γ. The formation of γ″ phase gradually improves the hardness of the material up to 650 h (224 HV) of ageing with a corresponding average precipitate size of 61 nm. The growth of γ″ particles complies with the Lifshitz–Slyozov–Wagner (LSW) theory of diffusion-controlled precipitate coarsening during the entire ageing period. Surprisingly, the hardness declined significantly beyond 650 h of ageing, even though the γ″ phase remained coherent with the matrix despite its coarsening (106 nm after 1000 h of ageing) and evidence of γ″→δ (mainly incoherent) transformation is not detectible throughout the ageing treatment. This lowering of hardness is attributed to a non-conventional slip-to-twin transition in the deformation mode of coherent γ″ particles after prolonged ageing, which is confirmed through tensile deformation micromechanisms analysis of the 650 and 1000 h aged samples.

Relevance of Fiscal Illusion Proposition and Wagner Theory to Nigerian Budget Performance (Nexus among Fiscal Illusion Index, Recurrent and Capital Budget)

This paper presents an empirical analysis of the consequences of fiscal illusion for public spending outcomes in a developing country context, specifically Nigeria, over the period 1993- 2022. The presence of fiscal illusion and its main indicators are identified (measured here through deficit illusion, and degree of tax visibility, where the real burden of taxation is underrepresented to the citizen-voter). We find that the Nigerian economy reveals significant fiscal illusion as measured in above terms. Also, fiscal illusion is found to have major and positive impact on the demand for government capital expenditure and government recurrent expenditure and consequently, on real government expenditure in the economy over the chosen time period. This work demonstrated that the controversial question involving the role of fiscal illusion practices on public finances is not recent, but can be thought of as deriving from the discussion invoked by Puviani (1903) and substantially enriched by Buchanan (1960). In spite of the fact that the ‘Fiscal Illusion’ School of Buchanan and Wagner (1977) identifies higher levels of fiscal illusion promoting increasing increments in the size of the public sector, this work developed a model that predicts higher levels of fiscal illusion also decrease national economic growth rates. The government additionally creates the false illusion that public expenditures are lower than they are in reality and for this reason it is easier to maintain the illusive fiscal discipline. On the one hand, the government may cut expenditures in an ostensible way and step towards reducing the budget deficit. On the other hand, without additional procedures the government may introduce new public expenditures outside the budget and, consequently, without any special control of the law-making arm of government.

Air entrapment at impact of a conus onto a liquid

In this experimental work, a conus impacts a deep liquid pool at a speed varying from 1.3 to $19.0\ {\rm cm}\ {\rm s}^{-1}$ . Two liquids (2.5 % butanol–water solution or distilled water) and four coni made from duralumin with a diameter of 180 mm and different deadrise angles $\beta$ ( $2^{\circ }$ , $3^{\circ }$ , $4^{\circ }$ and 5 $^{\circ }$ ) are tested. An air cushion is trapped between the conus solid surface and the liquid. Several types of bubble patterns after the collapse of the air cushion are observed: one or multiple bubbles near the conus centre (vertex), irregular trails of bubbles on the conus surface and a ring of bubbles in a ‘necklace’-shaped arrangement. With a total internal reflection set-up and appropriate image post-processing, the external and internal radii of the ring-shaped wetted area are estimated for each frame. The external (internal) radius increases (decreases) in time following a linear (exponential) law. The speed of the outer border of the wetted area is in agreement with the Wagner theory for a body impacting onto a liquid. The initial radius of the annular touchdown region is estimated as the intersection of the relevant fitting curves. In the studied range of parameters, the initial radius obeys a universal scaling law, which follows from the air–water lubrication–inertia balance.

Natural time analysis together with non-extensive statistical mechanics shorten the time window of the impending 2011 Tohoku [formula omitted]9 earthquake in Japan

Applying natural time analysis (NTA) to the Japanese seismic data, we have found that the system enters the critical stage upon the occurrence of M=4.2-5.0 earthquakes from 08:36 to 13:14 local time (LT) on 10 March 2011, i.e., almost one day before the M9 Tohoku earthquake on 11 March 2011. In addition, here, we find that just after this period the entropy change ΔS under time reversal of NTA along with the Tsallis entropy of non-extensive statistical mechanics (NESM) show distinct simultaneous changes. This simultaneous appearance enables the shortening of the time window of the impending mainshock to several hours. Furthermore, upon the occurrence of the M7.3 foreshock at 11:45 LT on 9 March 2011, the following fact emerged: The Tsallis entropy of NESM exhibited a scaling behavior with a characteristic exponent 1/3 that conforms to Lifshitz–Slyozov–Wagner theory for phase transitions as had been also observed in NTA for the fluctuations of the entropy change ΔS under time reversal upon a M7.8 earthquake occurrence in Japan on 22 December 2010. The latter obeyed the form A(t−t0)c where c is approximately equal to 1/3 and the pre-factors A are proportional to the scale i (number of events) while t0 is almost 0.2 days after this M7.8 earthquake.

Studies of structural, dielectric, and optical properties of CuCoFeO4 spinel for high frequency, microwave, and optoelectronic applications

In this study, we synthesized by the sol-gel method the CuCoFeO4 spinel and studied its structural, dielectric, and optical properties. The sample exhibits a regular cubic spinel structure (Fd3¯m space group). Semiconductor behavior with the CBH model was observed from the variation in electrical conductivity as a function of frequency and temperature. Summerfield scaling merges conductivity isotherms into a single master curve. Non-Debye relaxation is shown in the electric modulus of the prepared composition. The impedance spectra indicate the effects of both grain and grain boundary contributions on electrical properties. The impedance analysis is presented with electrical processes modeling in the sample. This is done using an equivalent circuit model comprising a parallel RC circuit for grains and grain boundaries. The obtained simulated results agree with the measured results. Maxwell-interfacial Wagner's polarization theory was used to explain dielectric constant change. The synthesized material exhibits low dielectric constants and dielectric losses at higher frequencies, as well as high electrical resistivity. These properties make CuCoFeO4 spinel a suitable candidate for high-frequency applications and microwave absorption devices. Moreover, CuCoFeO4 spinel presents low band gap energy, making it a suitable material for visible-light absorption.

CAPITAL SPENDING AND ECONOMIC GROWTH CORRELATION IN GEORGIA

Nino Mikeladze&#x0D; Email:ninomikeladze88@gmail.com&#x0D; Doctoral student (Master’s in Economics) Ivane Javakhishvili Tbilisi State University &#x0D; Tbilisi, Georgia&#x0D; https://orcid.org/0009-0008-1214-7241&#x0D; Government measures during the economic policy implementation should be based on the impact on economic growth and economic development. Moreover, as it is inevitable to have government expenditures, it is crucial to analyze what kind of relationship exists between economic growth and government expenditure. According to Keynes, government expenditure is the measure of the fiscal policy, On the other hand, according to Wagner, public spending is endogenous factor of economic development. There is no common attitude towards Wagner theory. Moreover, Wagner theory is considered to be valid for the long run period and results could be more valid in terms of economic as well as statistical interpretation, when longer time-series is taken. While exploting the dependence between economic growth and government spending, we should analyze the Armey-Rahn curve as well, which explains that up to some point, when government spending is increasing, economic activity is increasing as well, but then is starts to decline. The paper examines such dependence based on Wagner’s law and Keynes’s theory for Georgia, but using only capital spending as it is perceived as one of the main sources for economic growth. All the available data is used, during 1995-2022, for capital spending growth and economic growth indicators. &#x0D; The results show that Wagner’s law is not fulfilled meaning that economic growth is depended variable and capital spending growth is explanatory. The impact on economic growth is observed after 3 years, which makes sense if we consider the nature of capital spending. However, we can say that due to the lack of data and only two variables included in the analysis, the results might not be relevant.

The origin of different morphology of internal oxide precipitates in ferritic and austenitic steels

The internal oxide precipitates were supposed to be spherical in Wagner's original theory, while the following research demonstrated that this assumption is an exception rather than the truth, which caused deviations in the application of this theory. In this study, the internal oxide precipitates have a needle-like and a near-spherical morphology in a Fe-9Cr ferritic and a Fe-17Cr-9Ni austenitic steels after exposure to 600 °C deaerated steam for 600 h, respectively. The nano-to-atomic scale characterization shows that the morphology of the internal oxide precipitates is controlled by the structure of the interfaces between the metal matrix and the internal oxide, while the interface structure is mainly affected by the crystallographic structure of the two phases and their orientation relationship. In addition, the internal oxide precipitation-induced volume expansion and the outward Fe diffusion-induced volume shrink occur simultaneously during the oxidation process. The stress status in the internal oxidation zone (IOZ) is the competing result of the two factors, which could dynamically affect the high-temperature oxidation. The results obtained in this study suggest that there is potential to control the distribution, morphology, and interface structure of the internal oxide precipitates by selecting appropriate base metal and internal oxide-forming element, in order to obtain better high-temperature oxidation-resistant materials.

Phase-field modeling of alloy oxidation at high temperatures

Oxide growth is a complex process involving transport of reactive species, heterogeneous reactions, and microstructure evolution. Predicting oxidation kinetics, especially the oxide morphological change has been a longstanding challenge. Here we develop a phase-field model for predicting the oxide growth kinetics of a multicomponent alloy during high temperature oxidation, focusing on internal oxidation (non-protective) and its transition to external oxidation (protective). The predicted kinetics and oxide morphology are analyzed and compared to the classical Wagner's theory and an existing analytical model by Zhao and Gleeson. Some assumptions used in the analytical models and the limitation are discussed. In addition, it is demonstrated that the morphology and distribution of the initial oxide nuclei play an important role in the later stage oxide connectivity and thus the transition to external oxidation.

Kinetics of Precipitation Processes at Non-Zero Input Fluxes of Segregating Particles

We consider the process of formation and growth of clusters of a new phase in segregation processes in solid or liquid solutions in an open system when segregating particles are added continuously to it with a given rate of input fluxes, Φ. As shown here, the value of the input flux significantly affects the number of supercritical clusters formed, their growth kinetics, and, in particular, the coarsening behavior in the late stages of the process. The detailed specification of the respective dependencies is the aim of the present analysis, which combines numerical computations with an analytical treatment of the obtained results. In particular, a treatment of the coarsening kinetics is developed, allowing a description of the development of the number of clusters and their average sizes in the late stages of the segregation processes in open systems, which goes beyond the scope of the classical Lifshitz, Slezov and Wagner theory. As is also shown, in its basic ingredients, this approach supplies us with a general tool for the theoretical description of Ostwald ripening in open systems, or systems where the boundary conditions, like temperature or pressure, vary with time. Having this method at one's disposal supplies us with the possibility that conditions can be theoretically tested, leading to cluster size distributions that are most appropriate for desired applications.

Ostwald ripening of aqueous microbubble solutions.

Bubble solutions are of growing interest because of their various technological applications in surface cleaning, water treatment, and agriculture. However, their physicochemical properties, such as the stability and interfacial charge of bubbles, are not fully understood yet. In this study, the kinetics of radii in aqueous microbubble solutions are experimentally investigated, and the results are discussed in the context of Ostwald ripening. The obtained distributions of bubble radii scaled by mean radius and total number were found to be time-independent during the observation period. Image analysis of radii kinetics revealed that the average growth and shrinkage speed of each bubble is governed by diffusion-limited Ostwald ripening, and the kinetic coefficient calculated using the available physicochemical constants in the literature quantitatively agrees with the experimental data. Furthermore, the cube of mean radius and mean volume exhibit a linear time evolution in agreement with the Lifshitz-Slezov-Wagner (LSW) theory. The coefficients are slightly larger than those predicted using the LSW theory, which can be qualitatively explained by the effect of finite volume fraction. Finally, the slowdown and pinning of radius in the shrinkage dynamics of small microbubbles are discussed in detail.

The relationship between economic growth and government Expenditures from the perspective of Wagner's theory: Evidence of Nonlinear Approach in Iran's Economy

The relationship between economic growth and government Expenditures from the perspective of Wagner's theory: Evidence of Nonlinear Approach in Iran's Economy

Simulation of water entry into shallow water based on boundary element method

The problem of a two-dimensional wedge entering into shallow water is investigated with the boundary element method based on the potential flow theory, and fully nonlinear boundary conditions in time domain are imposed. A stretched coordinate system is used at the initial stage of water entry to avoid the numerical problems originated from extremely small wetted surface. An auxiliary function is used to calculate the pressure on the body surface. The free surface is updated through the fourth order Runge-Kutta scheme. Particularly, a jet cut model is used to avoid the numerical difficulties when the thin and high jet forms. Detailed results through the free surface, pressure distribution and hydrodynamic load at constant speed and prescribed time-varying speed are provided, the comparison with the results from experiments, Wagner theory, semi-analytic method are made and effects of water depth are investigated in detail. It is found that the bottom of the shallow water domain would exert a noticeable effect on the pressure distribution and force of the wedge, especially when the tip of wedge is close to the domain bottom.

Generalization of classical Hillert's grain growth and LSW theories to a wide family of kinetic evolution equations and stationary distribution functions

Coarsening of objects as grains or precipitates belongs to the most relevant processes during the heat treatment and high-temperature application of materials. Based on the appropriate models incorporating the relevant phenomena, the coarsening of objects can be described by evolution equations, which are reflected by stationary radius distribution functions. Such a distribution function for a distinct evolution equation has been derived e.g. in the frame of Lifshitz, Slyozov and Wagner (LSW) theory for the precipitate coarsening. The current evolution equations are in prevailing number of cases based on the mean field approach. A two-parametric family of evolution equations is proposed, which includes e.g. the LSW theory as a special case. The specific phenomena controlling the object evolution can be incorporated by using proper values of parameters used in the evolution equation. An effective procedure is presented how the corresponding stationary radius distribution function can be calculated for each evolution equation from the family. The distribution functions are demonstrated for several combinations of admissible parameters. Basic characteristics of their shapes are also evaluated.

Violent droplet impacts with non-flat surfaces

The application of Wagner theory to idealised two-dimensional inertially dominated droplet impacts is extended to incorporate non-flat substrates that are continuous functions of distance along the surface. Mixed boundary value problems are solved for the displacement and velocity potentials for both a single impact with an asymmetric substrate and a pair of impacts. The droplet free-surface position and the pressure on the wetted surface are calculated, along with the load and moment on the substrate. For double impacts a void may be formed between the substrate and the droplet free surface. Double impacts are compared with a single asymmetric impact with one half of the equivalent substrate geometry to assess how the free surface, loads and moments are affected by the separation between impact sites. Interactions between symmetric double impacts enhance the liquid penetration between the impact sites and increase the load and moment on each substrate element compared with the corresponding single impact. The time taken for the void between droplet and substrate to become saturated is found assuming the gas pressure build-up and capillary forces are negligible, giving an estimate for the transition time from a partially wetted to a fully wetted surface close to the initial impact site. After the void becomes saturated, the subsequent free-surface evolution is determined and the effect of periodic roughness on the contact line evolution is calculated. For surfaces formed of an array of asperities, secondary impacts which both traps further voids and completely wet the surface are found.